[EM] Re: Collecting Ordinal Information

[Simmons, Forest]

Below where I wrote "99% confidence" I should have specified the confidence interval:
 
If n= 10000,the the standard deviation is 100*SQRT(P*Q) which is less than 50, as long as P and Q are positive numbers that sum to unity.  Here P is the probability of one candidate being the preferred of the majority of the voters (not just the ten thousand randomly chosen to vote on this pairwise contest), and Q is the probability of the other candidate being the preferred.
 
A one sided 99 percent confidence interval corresponds to roughly 2.3 standard deviations, which, in this case would correspond to about 115 voters.  So if A beat B by as few as 115 out of ten thousand votes (i.e. by a little more than one percent of the vote) then we could be 99 percent confident that the same result would hold if the entire population of voters (from whom the 10000 had been randomly selected) had voted in that pairwise contest.
 
I submit that this is greater confidence than we now have in typical large races with that close of a result.
 
 
Forest
 
I had written ...
 
My idea is that in a large enough election, the individual pairwise contests could be farmed out at random to the voters.
 
...
 
To be specific, suppose that you had twenty single winner races with ten candidates each, and no ballot measures.
 
Each of the ten candidate races could be broken down into 45 pairwise contests, so the total number of pairwise contests would be 20*45=900.
 
If there were nine hundred thousand voters, and each of them received a random selection of ten pairwise contests to weigh in on, then each pairwise defeat would be based on ten thousand ballots, well above the statistical sample size requirement for 99% confidence.
 
 
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